Let S := {1, 2, 3, 4, 5, 6, 7, 8}, and let T be an unknown set. From the following, what can you conclude about T? Be as precise as possible: if you can list the elements of T exhaustively, do so; if...

Let S := {1, 2, 3, 4, 5, 6, 7, 8}, and let T be an unknown set. From the following, what can you conclude about T? Be as precise as possible: if you can list the elements of T exhaustively, do so; if you can’t, identify any elements that you can conclude must be (or must not be) in T.

1. |S × T| = 16 and h1, 2i,h3, 4i ∈ S × T

2. S × T = ∅

3. (S × T) ∩ (T × S) = {h3, 3i}

4. S × T = T × S